Observational and theoretical evidence points to the existence of an u
nusually high magnetic field on GX 1 + 4. The pulsar is thus an ideal
laboratory for studying two-photon cyclotron emission, an important so
urce of photons of frequency significantly less than the cyclotron fre
quency in X-ray pulsars. Low-frequency approximations to the two-photo
n cyclotron emission transition probabilities are derived. These are u
sed to calculate the theoretical opening angle of the double-humped pu
lse shape predicted by the two-photon cyclotron emission model. The th
eoretical pulse shape, incorporating the effects of gravitational ligh
t bending, is compared with observations of GX 1 + 4. Observed light c
urves have opening angles consistent with the theoretically predicted
maximum value.